Localised analytic torsion and relative analytic torsion for non compact Lie groups of type I

Let $G$ be a (non compact) connected simply connected locally compact second countable Lie group, either abelian or unimodular of type I, and $\rho$ an irreducible unitary representation of $G$. Then, we define the analytic torsion of $G$ localised at the representation $\rho$. Next, let $\Gamma$ a discrete cocompact subgroup of $G$. We use the localised analytic torsion to define the relative analytic torsion of the pair $(G,\Gamma)$, and we prove that it coincides with the Lott $L^2$ analytic torsion of a covering space. We illustrate these constructions analysing in some details two examples: the abelian case, and the case $G=H$, the Heisenberg group

A NEW HANDHELD SCANNER FOR 3D SURVEY OF SMALL ARTIFACTS: THE STONEX F6

Movable heritage preserved in our museums are an invaluable evidence of our past. In order to properly respond to the need of 3D documentation of these significant assets, in the last few years both range-based and image-based solutions have been developed by researchers operating in the framework of Geomatics with a special focus on reaching a high level of detail and on texture radiometric quality, taking into consideration the intrinsic fragility of these kinds of objects which during the survey require a contactless approach. During the presented research a collection of architectural models representing ancient Nubian temples from “Museo Egizio di Torino” had been digitalized using different techniques; in particular, the wooden maquette of the temple of El-Hilla has been acquired using a new structured light handheld laser scanner, the Stonex F6 SR, and applying a close-range photogrammetric approach. In this paper a comparison between the two approaches is proposed as regards acquisition workflow, final results and suitability as regards digitisation of objects belonging to movable heritage and museum collections

A note about the isotropy groups of 22-plane bundles over closed surfaces

Let $\xi$ be a $2$-plane bundle over a closed surface $S$. The line bundles $\lambda$ over $S$ such that $\xi\otimes\lambda\cong\xi$ form a group $\mathcal{J}(\xi)$ (the isotropy group of $\xi$); the scope of this paper is to describe $\mathcal{J}(\xi)$

wake measurements behind an oscillating airfoil in dynamic stall conditions

The unsteady flow field in the wake of an NACA 23012 pitching airfoil was investigated by means of triple hot-wire probe measurements. Wind tunnel tests were carried out both in the light and deep dynamic stall regimes. The analysis of the wake velocity fields was supported by the measurements of unsteady flow fields and airloads. In particular, particle image velocimetry surveys were carried out on the airfoil upper surface, while the lift and pitching moments were evaluated integrating surface pressure measurements. In the light dynamic stall condition, the wake velocity profiles show a similar behaviour in upstroke and in downstroke motions as, in this condition, the flow on the airfoil upper surface is attached for almost the whole pitching cycle and the airloads show a small amount of hysteresis. The deep dynamic stall measurements in downstroke show a large extent of the wake and a high value of the turbulent kinetic energy due to the passage of strong vortical structures, typical of this dynamic stall regime. The comprehensive experimental database can be considered a reference for the development and validation of numerical tools for such peculiar flow conditions

Zeta function regularization for a scalar field in a compact domain

We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas for the partition function of the associated physical model at low and high temperature for any compact domain $M$. Furthermore, we provide an exact formula for the zeta function at any value of $r$ when $M$ is a $D$-dimensional box or a $D$-dimensional torus; this allows a rigorous calculation of the zeta invariants and the analysis of the main thermodynamic functions associated to the physical models at finite temperature.Comment: 19 pages, no figures, to appear in J. Phys.

FROM ARCHIVE DOCUMENTATION TO ONLINE 3D MODEL VISUALIZATION OF NO LONGER EXISTING STRUCTURES: THE TURIN 1911 PROJECT

Rebuilding the past of cultural heritage through digitization, archiving and visualization by means of digital technology is becoming an emerging issue to ensure the transmission of physical and digital documentation to future generations as evidence of culture, but also to enable present generation to enlarge, facilitate and cross relate data and information in new ways. In this global effort, the digital 3D documentation of no longer existing cultural heritage can be essential for the understanding of past events and nowadays, various digital techniques and tools are developing for multiple purposes. In the present research the entire workflow, starting from archive documentation collection and digitization to the 3D models metrically controlled creation and online sharing, is considered. The technical issues to obtain a detail 3D model are examined stressing limits and potentiality of 3D reconstruction of disappeared heritage and its visualization exploiting three complexes belonging to 1911 Turin World’s Fair

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

"TORINO 1911" project: A contribution of a SLAM-based survey to extensive 3D heritage modeling

In the framework of the digital documentation of complex environments the advanced Geomatics researches offers integrated solution and multi-sensor strategies for the 3D accurate reconstruction of stratified structures and articulated volumes in the heritage domain. The use of handheld devices for rapid mapping, both image- and range-based, can help the production of suitable easy-to use and easy-navigable 3D model for documentation projects. These types of reality-based modelling could support, with their tailored integrated geometric and radiometric aspects, valorisation and communication projects including virtual reconstructions, interactive navigation settings, immersive reality for dissemination purposes and evoking past places and atmospheres. The aim of this research is localized within the “Torino 1911” project, led by the University of San Diego (California) in cooperation with the PoliTo. The entire project is conceived for multi-scale reconstruction of the real and no longer existing structures in the whole park space of more than 400,000 m², for a virtual and immersive visualization of the Turin 1911 International “Fabulous Exposition” event, settled in the Valentino Park. Particularly, in the presented research, a 3D metric documentation workflow is proposed and validated in order to integrate the potentialities of LiDAR mapping by handheld SLAM-based device, the ZEB REVO Real Time instrument by GeoSLAM (2017 release), instead of TLS consolidated systems. Starting from these kind of models, the crucial aspects of the trajectories performances in the 3D reconstruction and the radiometric content from imaging approaches are considered, specifically by means of compared use of common DSLR cameras and portable sensors

THE IPAD PRO BUILT-IN LIDAR SENSOR: 3D RAPID MAPPING TESTS AND QUALITY ASSESSMENT

The main goal of this ongoing research is the evaluation of the iPad Pro built-in LiDAR sensor for large scale 3D rapid mapping. Different aspects have been considered from the architectural surveying perspective and several analyses were carried out focusing on the acquisition phase and the definition of best practices for data collection, the quantitative analysis on the acquired data and their 3D positional accuracy assessment, and the qualitative analysis of the achievable metric products. Despite this paper is a preliminary analysis and deeper studies in various application environment are necessary, the availability of a LiDAR sensor embedded in a tablet or mobile phone, appears promising for rapid surveying purposes. According to test outcomes, the sensor is able to rapidly acquire reliable 3D point clouds suitable for 1:200 architectural rapid mapping; the iPad Pro could represent an interesting novelty also thanks to its price (compared to standard surveying instruments), portability and limited time required both for data acquisition and processing